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Numerical Analysis and Computation Commons™
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Full-Text Articles in Numerical Analysis and Computation
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Rose-Hulman Undergraduate Mathematics Journal
A system of first-order differential equations that arises in a model for the growth of microorganisms in a chemostat with Monod kinetics is studied. A new, semi-implicit numerical scheme is proposed to approximate solutions to the system. It is shown that the scheme is uniquely solvable and unconditionally stable, and further properties of the scheme are analyzed. The convergence rate of the numerical solution to the true solution of the system is given, and it is shown convergence of the numerical solutions to the true solutions is uniform over any interval [0, T ] for T > 0.
Flexible Memory Allocation In Kinetic Monte Carlo Simulations, Aaron David Craig
Flexible Memory Allocation In Kinetic Monte Carlo Simulations, Aaron David Craig
Masters Theses
We introduce two new algorithms for Kinetic Monte Carlo simulations: the minimal and flexible allocation algorithms. The theory and computational challenges associated with K.M.C. simulations are briefly discussed. We outline the simple cubic, solid-on-solid model of epitaxial growth and analyze four methods for its simulation: the linear search, standard inverted list, minimal allocation, and flexible allocation algorithms. We then implement these algorithms, analyze their performances, and discuss implications of the results.